[Reconstruction précise de la vitesse pour des approximations par la méthode de Galerkine discontinue d'écoulements diphasiques en milieu poreux]
Nous considérons une méthode de Galerkine discontinue pour approcher les écoulements diphasiques non-miscibles en milieu poreux dans la formulation en pression globale. Une approche séquentielle est utilisée avec un schéma d'Euler implicite pour l'équation de la saturation, le même ordre polynomial pour la pression et la saturation, et en l'absence de limiteurs. Nous montrons comment reconstruire à partir de l'équation en pression une vitesse totale précise pour l'équation de la saturation. Des exemples numériques illustrent les avantages de l'approche proposée.
We consider Discontinuous Galerkin approximations of two-phase, immiscible porous media flows in the global pressure/fractional flow formulation with capillary pressure. A sequential approach is used with a backward Euler step for the saturation equation, equal-order interpolation for the pressure and the saturation, and without any limiters. An accurate total velocity field is recovered from the global pressure equation to be used in the saturation equation. Numerical experiments show the advantages of the proposed reconstruction.
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@article{CRMATH_2009__347_9-10_551_0,
author = {Ern, Alexandre and Mozolevski, Igor and Schuh, L.},
title = {Accurate velocity reconstruction for {Discontinuous} {Galerkin} approximations of two-phase porous media flows},
journal = {Comptes Rendus. Math\'ematique},
pages = {551--554},
publisher = {Elsevier},
volume = {347},
number = {9-10},
year = {2009},
doi = {10.1016/j.crma.2009.02.011},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2009.02.011/}
}
TY - JOUR AU - Ern, Alexandre AU - Mozolevski, Igor AU - Schuh, L. TI - Accurate velocity reconstruction for Discontinuous Galerkin approximations of two-phase porous media flows JO - Comptes Rendus. Mathématique PY - 2009 SP - 551 EP - 554 VL - 347 IS - 9-10 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2009.02.011/ DO - 10.1016/j.crma.2009.02.011 LA - en ID - CRMATH_2009__347_9-10_551_0 ER -
%0 Journal Article %A Ern, Alexandre %A Mozolevski, Igor %A Schuh, L. %T Accurate velocity reconstruction for Discontinuous Galerkin approximations of two-phase porous media flows %J Comptes Rendus. Mathématique %D 2009 %P 551-554 %V 347 %N 9-10 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2009.02.011/ %R 10.1016/j.crma.2009.02.011 %G en %F CRMATH_2009__347_9-10_551_0
Ern, Alexandre; Mozolevski, Igor; Schuh, L. Accurate velocity reconstruction for Discontinuous Galerkin approximations of two-phase porous media flows. Comptes Rendus. Mathématique, Tome 347 (2009) no. 9-10, pp. 551-554. doi : 10.1016/j.crma.2009.02.011. http://www.numdam.org/articles/10.1016/j.crma.2009.02.011/
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